scipy.fft.idst(x, type=2, n=None, axis=- 1, norm=None, overwrite_x=False, workers=None, orthogonalize=None)[source]#

Return the Inverse Discrete Sine Transform of an arbitrary type sequence.


The input array.

type{1, 2, 3, 4}, optional

Type of the DST (see Notes). Default type is 2.

nint, optional

Length of the transform. If n < x.shape[axis], x is truncated. If n > x.shape[axis], x is zero-padded. The default results in n = x.shape[axis].

axisint, optional

Axis along which the idst is computed; the default is over the last axis (i.e., axis=-1).

norm{“backward”, “ortho”, “forward”}, optional

Normalization mode (see Notes). Default is “backward”.

overwrite_xbool, optional

If True, the contents of x can be destroyed; the default is False.

workersint, optional

Maximum number of workers to use for parallel computation. If negative, the value wraps around from os.cpu_count(). See fft for more details.

orthogonalizebool, optional

Whether to use the orthogonalized IDST variant (see Notes). Defaults to True when norm=="ortho" and False otherwise.

New in version 1.8.0.

idstndarray of real

The transformed input array.

See also


Forward DST



For type in {2, 3}, norm="ortho" breaks the direct correspondence with the inverse direct Fourier transform.

For norm="ortho" both the dst and idst are scaled by the same overall factor in both directions. By default, the transform is also orthogonalized which for types 2 and 3 means the transform definition is modified to give orthogonality of the DST matrix (see dst for the full definitions).

‘The’ IDST is the IDST-II, which is the same as the normalized DST-III.

The IDST is equivalent to a normal DST except for the normalization and type. DST type 1 and 4 are their own inverse and DSTs 2 and 3 are each other’s inverses.